propositional logic equivalence proof
Hi all, I have to do a proof and I keep hitting dead ends.
The proof is:
"Show the following general statements are equivalent. ( and are sets of formulas and is a formula.)
(E) For all , if every finite subset of is satisfiable, then so is .
(F) For all and , if then , for some finite subset of ."
I want to prove (E) --> (F) and then (F) --> (E), but I feel like I keep proving the converse of what I want to prove.
I thought I could try using the contrapositives of these statements, or try a proof by contradiction, but nothing seems to be working in the right direction.